157 citations · 642 across the 35 of their papers we have counts for
8 papers · 1 filter
Three-term arithmetic progressions and sumsets
Tom Sanders
Suppose that G is an abelian group and A is a finite subset of G containing no three-term arithmetic progressions. We show that |A+A| >> |A|(log |A|)^{1/3-ε} for all ε>0.
A quantitative version of the idempotent theorem in harmonic analysis
Ben Green, Tom Sanders
Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure μin M(G) is said to be i…
An application of a local version of Chang's theorem
Tom Sanders
We prove a theorem claimed in math.CA/0605519 which asserts that if A is a subset of a compact abelian group G with density of a particular (natural, although technical) form then…
Boolean functions with small spectral norm
Ben Green, Tom Sanders
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be ex…
A note on Freiman's theorem in vector spaces
Tom Sanders
We show that if A is a subset of F_2^n and |A+A| < K|A| then A is contained in a subspace of size at most 2^{O(K^{3/2}log K)}|A|. This improves on the previous best of 2^{O(K^2)}.
The Littlewood-Gowers problem
Tom Sanders
We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic fu…